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Confidential | 2 Energy Exemplar, LLC PLEXOS for Power Systems Released in 1999 Continuously Developed to meet Challenges of a Dynamic Environment A Global Leader in Energy Market Simulation Software With Over 200 Installations in 17 Countries Offices in Adelaide, Australia; London, UK; California, USA High Growth Rate in Customers and Installations Staff Expertise in Operations Research, Electrical Engineering, Economics, Mathematics, Statistics with over 20% Ph.Ds North American Office: Consulting Customer Support Training Software Sales North American Datasets/WECC Term 01/25/13

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Transmission Expansion General Description: The planned addition/deletion of AC and DC lines from the system is supported by all OPF methods in PLEXOS using the Line [Units] property. PLEXOS automatically recomputes the shift factors required to cope with the changes in topography. LT Plan supports all types of transmission constraints including security-constrained optimal power flow. Optimized transmission line expansion (using the [Max Units Built] property), retirement (using the [Max Units Retired] property) in LT Plan works in much the same way as generation expansion – with the restriction that only DC lines can be considered. This restriction exists due to computational burden that would be imposed by the need to recompute the OPF when considering combinations of AC line configurations. Expansion of the AC network can be approximated by: – use of DC lines i.e. by removing the Line [Reactance] property from the expansion candidates; and/or – using Interface expansion (see below) in which the underlying AC network is preserved and expansion in done in a continuous manner on selected flow branches 1501/25/13

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COM - Microsoft Component Object Model technology. – A Microsoft designed framework for program interoperability. Many programming environments allow COM compliant calls, including VBA in Office. – PLEXOS COM provides functions to change input, execute models and projects, and query solutions.NET - Microsoft.NET Framework. – A programming framework for application development. Resulting programs are easier to produce and maintain, more consistent and less prone to bugs. They require.NET to run – PLEXOS uses.NET API - Application Programming Interface. – A series of embedded system calls and a defined object model that allows programmers to access and modify applications. A good example is the Excel object model in VBA which allows programmers to modify the way Excel function by embedding code. – PLEXOS has an API accessible through.NET compliant programming environments like Visual Studio – PLEXOS API allows for customization and process control AMMO - ActiveX Mathematical Modeling Objects – Proprietary Optimization layer in PLEXOS. – Interface AMMO to customize simulations using VS.NET 17 Application Programming Interface Many Microsoft and Other Windows-based environments allow connections to COM compliant applications including PLEXOS. PLEXOS can be automated from many environments, including Office and SQLServer 01/25/13

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18 OpenPlexos System Calls CallFunctionWhen MyRegion.price()Overrides Regional pricingEvery Pricing Event MyModel.afterinitializeAdd custom objects and/or constraints Once per simulation phase after Built-in Objects are initialized MyModel.AfterPropertiesModify constraint coefficients add custom Variables and Constraints At least once per step after mathematical program is fully populated MyModel.BeforeOptimizeOverride Solver SettingsAt least once per step before the solver is called MyModel.AfterOptimizeRe-simulation Overrides.At least once per step after the solver has completed MyModel.OnWarningTrap Warning/error conditionsWhen any warning message is raised MyModel.EnforceMyConstraintsCheck and enforce customized constraints Called during Transmission Convergence MyModel.BeforeRecordSolutionOverrides for generator bidding, uplift etc. which may call for re-optimization Once per step after completion, but before output is written MyModel.AfterRecordSolutionCustomized reporting.Once per step after the Model output is written 01/25/13

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Risk Premium: expected increase in cost above mean value of the portfolio Risk Adjusted Value: the expected value plus the risk premium Risk Reduction Value is the difference in the risk adjusted value of portfolios 01/25/1320 Introducing Risk While the expected value of a renewable portfolio is higher than the cost of a traditional portfolio, renewables often come with risk attributes (i.e. low cost energy). The true cost of the renewable portfolio is less due to these risk attributes

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Measurement Issues: Deterministic provides a measure of value at given conditions: – Value of portfolio given average conditions Stochastic measures values of all measured conditions weighted by probabilities – Average value of portfolio given all conditions 01/25/1321 Risk Adjusted Values Why use Risk in Planning Decisions? It is likely that decisions made under deterministic planning, while optimal for the deterministic case, yield a decision which is costly under other known risks What is the Risk Adjusted Value?

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The Perfect Foresight Problem: Stochastic Run is simply a deterministic (predictable) run using randomly drawn data Optimization therefore assumes that you know the outcome, i.e. have perfect foresight What if you need to make a decision (UC, Hydro schedule, Build/retire), based on an unknown future? Stochastic Optimization makes the decision, then evaluates then runs stochastic optimizations, allowing the best decision to be determined 01/25/1322 Short-Comings of Deterministic Simulation

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Fix perfect foresight issue – Monte Carlo simulation can tell us what the optimal decision is for each of a number of possible outcomes assuming perfect foresight for each scenario independently; – It cannot answer the question: what decision should I make now given the uncertainty in the inputs? Stochastic Programming – The goal of SO is to find some policy that is feasible for all (or almost all) of the possible data instances and maximize the expectation of some function of the decisions and the random variables Scenario-wise decomposition – The set of all outcomes is represented as “scenarios”, the set of scenarios can be reduced by grouping like scenarios together. The reduced sample size can be run more efficiently 23 Stochastic Optimization (SO) 01/25/13 Confidential & Proprietary Information

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SO Theory The most widely applied and studied stochastic programming models are two-stage linear programs Here the decision maker takes some action in the first stage, after which a random event occurs affecting the outcome of the first-stage decision A recourse decision can then be made in the second stage that compensates for any bad effects that might have been experienced as a result of the first-stage decision The optimal policy from such a model is a single first-stage policy and a collection of recourse decisions (a decision rule) defining which second- stage action should be taken in response to each random outcome 2401/25/13

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SO Theory, Continued Where the first (or second) stage decisions must take integer values we have a stochastic integer programming (SIP) problem SIP problems are difficult to solve in general Assuming integer first-stage decisions (e.g. “how many generators of type x to build” or “when do a turn on/off this power plant”) we want to find a solution that minimises the total cost of the first and second stage decisions A number of solution approaches have been suggested in the literature PLEXOS uses scenario-wise decomposition /25/13

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SO in Unit Commitment Consider the unit commitment decision: Must make unit commitment decisions in Day-Ahead – First Stage Uncertainties such as load or wind: – Unknown Day-Ahead – More information Hour Ahead – Real-time is what it is Simulation using independent samples on the load and wind outcomes provides an optimal solution given each outcome – Perfect Foresight – UC Results differ in different scenarios Simulation using Stochastic Optimization provides an optimal solution given all outcomes (held back case) Cost of Perfect Information is the difference between a backcast case and the held back case 3001/25/13

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Day-ahead Unit Commitment Example CAPACITY TECHNICAL LIMITATIONS MINIMUM PRODUCTION PRODUCTION COST 2x100 [MW] -12hrs off -8hrs on [65] MW10$/MWh 100 [MW] -4hrs on -2hrs off [10] MW50$/MWh [MW] uncertain Must-run!-0$/MWh How to efficiently schedule thermal power plants with technical restrictions if we don’t know how much wind (and/or load) is going to be available? 3101/25/13

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Day-ahead Unit Commitment, Continued Assume for example a worst-case scenario analysis. First, the wind is absent during the entire day (pessimistic) Two base load “slow” units can be scheduled Fast units are required just in order to meet the load No wind generation is available 3201/25/13

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Day-ahead Unit Commitment, Continued Now assume an optimistic scenario analysis. Wind is going to be available during the entire day One base load “slow” unit pre-schedule Fast units in order to avoid unserved energy High wind resources The question is: If we don’t know how the wind is going to be… what to do? Dispatch one or two slow base units? 3301/25/13

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Day-ahead Unit Commitment, Continued Stochastic Optimisation: Two stage scenario-wise decomposition Take the optimal decision 2 Expected cost of decisions 1+2 Is there a better Decision 1? Take Decision 1 Reveal the many possible outcomes Stage 1: Commit 1 or 2 or none of the “slow” generators Stage 2: There are hundreds of possible wind speeds. For each wind profile, decide the optimal commitment of the other units and dispatch of all units 34 RESULT: Optimal unit commitment for “slow” generator 01/25/13

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Real (active) Power (P) – Does the work – Measured in Watts – If loads are purely resistive, then 100% or real power is transferred to loads Imaginary (reactive) Power (Q) (Wattless) – Does no work – Created by capacitance (leading) and inductance (lagging) and cancel each other – Moves the angle between voltage and current, Φ VI – measured in kilovolt-amperes reactive (KVAR), – If loads are purely reactive (i.e. voltage and current 90 0 out of phase), there is 0 real power transfer to loads 35 Alternating Current (AC) Source: Wikipedia 01/25/13

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37 AC Power Flows AC Power flows are solved via iterative methods such as Newton-Raphson, but: – Convergence is not guaranteed – Subject to high degree of infeasibilities – Extremely difficult to solve from cold-start However, an AC-OPF can be simplified, if: – Susceptance is large relative to impedance (resistance on circuit is small, relative to reactance) – Phase Angle differences are small (i.e. power factors are corrected) – Voltages are maintained at near identical magnitudes (hence voltage support) Simplified equation is linear and more easily solved – B y (n,m) = susceptance (1/reactance) on line between nodes n,m – ϕ n -ϕ m = difference in phase angles between nodes = cos(pf n ) - cos(pf m ) AC Power Flows for active and reactive Power injections at each node for a single phase system Linearized power flows after simplifying assumptions, b y (n,m) = reactance 01/25/13

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38 AC Power Flows Active power injection: the product of magnitude of the injected current |I|, voltage magnitude |V| at the bus and the cosine of the phase angle θ VI P = |V| |I| cos θ VI Reactive Power Injection: the product of magnitude of the injected current |I|, voltage magnitude |V| at the bus and the sin of the phase angle θ VI Q = |V||I|sinθ VI Active power flows from bus with larger voltage phase angle to bus with smaller voltage phase angle Reactive power flows from the bus with higher voltage magnitude to those with lower voltage magnitude – Reactive Flows not considered n DC-OPF – Voltage is tightly controlled in power systems operations 01/25/13

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Non-Physical Losses (NPL) (Piecewise Linear) Each loss tranche becomes a separate decision variable No built-in logic to be taken up in flow order. Losses may not be minimized, when there is a Dump-energy condition due to over-generation. – Typical Causes: Generator must-run constraints System security constraints Other constraints that force flows or generation against economic dispatch. – The optimization then prefers to increase losses near the node Chooses higher loss tranches first “getting away” from the original quadratic loss function. Requires Integer variables Requires iterative solutions (time consuming) These additional losses are referred to as non-physical losses 4001/25/13